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We extend HPQCDs earlier $n_f=4$ lattice-QCD analysis of the ratio of $overline{mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $overline{m}_b(mu)/overline{m}_c(mu)=4.586(12)$ at renormalization scale $mu=3$,GeV. This result is nonperturbative. Combining it with HPQCDs recent lattice QCD$+$QED determination of $overline{m}_c(3mathrm{GeV})$ gives a new value for the $b$-quark mass: $overline{m}_b(3mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $overline{m}_b(overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED.
We prove that the moduli spaces of curves of genus 22 and 23 are of general type. To do this, we calculate certain virtual divisor classes of small slope associated to linear series of rank 6 with quadric relations. We then develop new tropical metho
We provide a new geometric interpretation of the multidegrees of the (iterated) Kapranov embedding $Phi_n:overline{M}_{0,n+3}hookrightarrow mathbb{P}^1times mathbb{P}^2times cdots times mathbb{P}^n$, where $overline{M}_{0,n+3}$ is the moduli space of
While lattice QCD allows for reliable results at small momentum transfers (large quark separations), perturbative QCD is restricted to large momentum transfers (small quark separations). The latter is determined up to a reference momentum scale $Lamb
In this work we study the tau-function $Z^{1D}$ of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of $overline{mathcal M}_{g,n}$. The first
We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of $overline{mathcal{M}}_{g,n}$ is not pseudo-effective in some range, implying that $overline{mathcal{M}}_{12,6},overline{